Summary of Novel Kernel Models and Exact Representor Theory For Neural Networks Beyond the Over-parameterized Regime, by Alistair Shilton et al.
Novel Kernel Models and Exact Representor Theory for Neural Networks Beyond the Over-Parameterized Regime
by Alistair Shilton, Sunil Gupta, Santu Rana, Svetha Venkatesh
First submitted to arxiv on: 24 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Artificial Intelligence (cs.AI); Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper presents two models for training neural networks, applicable to networks of arbitrary width, depth, and topology. The first model is exact and global, casting the network as an element in a reproducing kernel Banach space, allowing for tight bounds on Rademacher complexity. The second model is exact and local, casting changes in network function due to weight and bias updates in a reproducing kernel Hilbert space, providing insight into model adaptation through tight bounds on Rademacher complexity. Additionally, the paper proves that the neural tangent kernel is a first-order approximation of the local-intrinsic neural kernel. The authors also present an exact novel representor theory for layer-wise neural network training with unregularized gradient descent in terms of a local-extrinsic neural kernel. This theory provides insight into the role of higher-order statistics in neural network training and the effect of kernel evolution. Throughout the paper, feedforward ReLU networks and residual networks (ResNet) are used as illustrative examples. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about two new ways to train neural networks that can be applied to any type of network. The first method is like a blueprint for understanding how the network works, while the second method focuses on what happens when we make small changes to the network. The authors also show that one of these methods is a good approximation of another. This helps us understand how neural networks adapt and change over time. The paper uses simple examples to explain these ideas. |
Keywords
» Artificial intelligence » Gradient descent » Neural network » Relu » Resnet
